WASHINGTON — Supreme Court nominee Elena Kagan won praise Thursday from a former critic, Democratic Sen. Arlen Specter of Pennsylvania, building momentum toward what for now appears a smooth road to confirmation this summer.

Specter is days from a tough primary. His reaction suggested Kagan, the solicitor general who President Barack Obama named to replace retiring Justice John Paul Stevens, could win a convert in her campaign for the votes she needs to be confirmed.

Even without the Pennsylvanian's support, Kagan is likely to be confirmed in the coming months by a Senate where Democrats have more than enough votes to prevail and Republicans are showing little appetite for a Supreme Court showdown. But Kagan and the White House are leaving nothing to chance.

Specter, a Republican when he voted against confirming Kagan to her current job, has said he opposed her then because she wouldn't answer questions about how she'd approach cases.

This time, Specter said, Kagan responded to specific questions, even criticizing a January Supreme Court ruling that upheld the First Amendment rights of corporations and labor unions to spend money on campaign ads, thus enhancing their ability to influence federal elections.

"She said she thought the court was not sufficiently deferential to Congress," Specter said outside his Capitol office after meeting with Kagan. He gave no commitment to back Kagan, although he called her "a good candidate" with excellent credentials.

"It was a very good meeting, and I think she was very forthcoming," Specter said.

Kagan stood by her past criticism of the Supreme Court confirmation process during the meeting, according to Specter, including her description of it as a "charade" in which nominees stonewall questions.

Kagan's session with Specter came near the start of a second full day of meetings with senators in both parties on Capitol Hill. She said she's beginning to get accustomed to the delicate ritual of closely watched courtesy calls she must make in the run-up to her summer confirmation hearings.

Kagan, 50, called on eight senators Wednesday and plans meetings with another seven on Thursday.

In the closed-door meetings, Kagan has assured senators that she's up to the job of being a justice, seeking to counter GOP criticism of her lack of experience as a judge or courtroom litigator.

Kagan, a former Harvard Law School dean, is also defending herself against Republican doubts about her fitness to be a fair justice. She said she'd be "faithful to the law," according to Sen. Jeff Sessions, R-Ala., who said he asked her whether she could be impartial given that she's identified with liberal positions and has clerked for two judges he called activist.

Sessions, the top Republican on the Judiciary panel that will hold Kagan's confirmation hearings, said he'd do his best to give her a fair hearing, and Sen. Patrick Leahy, D-Vt., the committee chairman, said he'd guarantee a process where senators could ask "all relevant questions."

Leahy and Sessions on Thursday sent Kagan a detailed, 10-page questionnaire — a routine step for judicial nominees — with questions ranging from her birthplace to potential conflicts of interest she could face on the court.

Republicans are questioning whether Kagan can be impartial in light of her political views and current position on Obama's team. And they have harshly criticized her decision while at Harvard to bar military recruiters from campus because she disagreed with the military's "don't ask, don't tell" policy on gay soldiers.

GOP senators say they want to see documents from her time serving in Bill Clinton's White House to get a better understanding of her fitness for the Supreme Court.

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